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Bombal Gordón, Fernando and Hernando Boto, Beatriz
(1995)
*On the injection of a Köthe function space into L 1 (μ).*
Commentationes mathematicae, 35
.
pp. 49-60.
ISSN 0373-8299

## Abstract

Operators from a Banach space X into a Banach space Y weaker than isomorphisms and, nevertheless, preserving some isomorphic property, i.e. such that a good property of Y lifts to X, have been studied by many authors. This note is also devoted to that study; more precisely, given a complete σ-finite measure space (Ω,Σ,μ) into L1(μ) and given necessary and sufficient conditions for such an operator to be a Tauberian or semi-Tauberian operator, a semi-embedding or a ∗∗-injection, in the case when X is an Orlicz space, it is also proved that these conditions are equivalent to the reflexivity of X. The results obtained are applied to deduce properties of the vector-valued Köthe function space X(E), E a Banach space, from the corresponding properties of L1(μ,E).

Item Type: | Article |
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Uncontrolled Keywords: | Köthe function |

Subjects: | Sciences > Mathematics > Differential geometry Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 20045 |

Deposited On: | 21 Feb 2013 15:49 |

Last Modified: | 21 Feb 2013 15:49 |

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